Tail associations in ecological variables and their impact on extinction risk

Insights Into Spatial Synchrony Enabled by Long-Term Data

Spatial synchrony, the tendency for temporal fluctuations in an ecological variable to be positively associated in different locations, is a widespread and important phenomenon in ecology. Understanding of the nature and mechanisms of synchrony, and how synchrony is changing, has developed rapidly over the past 2 decades. Many recent developments have taken place through the study of long-term data sets. Here, we review and synthesise some important recent advances in spatial synchrony, with a focus on how long-term data have facilitated new understanding. Longer time series do not just facilitate better testing of existing ideas or more precise statistical results; more importantly, they also frequently make possible the expansion of conceptual paradigms. We discuss several such advances in our understanding of synchrony, how long-term data led to these advances, and how future studies can continue to improve the state of knowledge.

Temporal turnover in species' ranks can explain variation in Taylor's slope for ecological timeseries

The scaling exponent relating the mean and variance of the density of individual organisms in space (i.e., Taylor's slope: zspace) is well studied in ecology, but the analogous scaling exponent for temporal datasets (ztime) is underdeveloped. Previous theory suggests the narrow distribution of ztime (e.g., typically 1-2) could be due to interspecific competition. Here, using 1694 communities time series, we show that ztime can exceed 2, and reaffirm how this can affect our inference about the stabilizing effect of biodiversity. We also develop a new theory, based on temporal change in the ranks of species abundances, to help account for the observed ztime distribution. Specifically, we find that communities with minimal turnover in species' rank abundances are more likely to have higher ztime. Our analysis shows how species-level variability affects our inference about the stability of ecological communities.

Asymmetric relationships and their effects on coexistence

Species coexistence attracts wide interest in ecology. Modern coexistence theory (MCT) identifies coexistence mechanisms, one of which, storage effects, hinges on relationships between fluctuations in environmental and competitive pressures. However, such relationships are typically measured using covariance, which does not account for the possibility that environment and competition may be more related to each other when they are strong than when weak, or vice versa. Recent work showed that such 'asymmetric tail associations' (ATAs) are common between ecological variables, and are important for extinction risk, ecosystem stability, and other phenomena. We extend MCT, decomposing storage effects to show the influence of ATAs. Analysis of a simple model and an empirical example using diatoms illustrate that ATA influences can be comparable in magnitude to other mechanisms of coexistence and that ATAs can make the difference between species coexistence and competitive exclusion. ATA influences may be an important new mechanism of coexistence.

Tail-dependent spatial synchrony arises from nonlinear driver-response relationships

Spatial synchrony may be tail-dependent, that is, stronger when populations are abundant than scarce, or vice-versa. Here, 'tail-dependent' follows from distributions having a lower tail consisting of relatively low values and an upper tail of relatively high values. We present a general theory of how the distribution and correlation structure of an environmental driver translates into tail-dependent spatial synchrony through a non-linear response, and examine empirical evidence for theoretical predictions in giant kelp along the California coastline. In sheltered areas, kelp declines synchronously (lower-tail dependence) when waves are relatively intense, because waves below a certain height do little damage to kelp. Conversely, in exposed areas, kelp is synchronised primarily by periods of calmness that cause shared recovery (upper-tail dependence). We find evidence for geographies of tail dependence in synchrony, which helps structure regional population resilience: areas where population declines are asynchronous may be more resilient to disturbance because remnant populations facilitate reestablishment.

Species relationships in the extremes and their influence on community stability

Synchrony among population fluctuations of multiple coexisting species has a major impact on community stability, i.e. on the relative temporal constancy of aggregate properties such as total community biomass. However, synchrony and its impacts are usually measured using covariance methods, which do not account for whether species abundances may be more correlated when species are relatively common than when they are scarce, or vice versa. Recent work showed that species commonly exhibit such 'asymmetric tail associations'. We here consider the influence of asymmetric tail associations on community stability. We develop a 'skewness ratio' which quantifies how much species relationships and tail associations modify stability. The skewness ratio complements the classic variance ratio and related metrics. Using multi-decadal grassland datasets, we show that accounting for tail associations gives new viewpoints on synchrony and stability; e.g. species associations can alter community stability differentially for community crashes or explosions to high values, a fact not previously detectable. Species associations can mitigate explosions of community abundance to high values, increasing one aspect of stability, while simultaneously exacerbating crashes to low values, decreasing another aspect of stability; or vice versa. Our work initiates a new, more flexible paradigm for exploring species relationships and community stability. This article is part of the theme issue 'Synchrony and rhythm interaction: from the brain to behavioural ecology'.

A new approach to interspecific synchrony in population ecology using tail association

Standard methods for studying the association between two ecologically important variables provide only a small slice of the information content of the association, but statistical approaches are available that provide comprehensive information. In particular, available approaches can reveal tail associations, that is, accentuated or reduced associations between the more extreme values of variables. We here study the nature and causes of tail associations between phenological or population-density variables of co-located species, and their ecological importance. We employ a simple method of measuring tail associations which we call the partial Spearman correlation. Using multidecadal, multi-species spatiotemporal datasets on aphid first flights and marine phytoplankton population densities, we assess the potential for tail association to illuminate two major topics of study in community ecology: the stability or instability of aggregate community measures such as total community biomass and its relationship with the synchronous or compensatory dynamics of the community's constituent species; and the potential for fluctuations and trends in species phenology to result in trophic mismatches. We find that positively associated fluctuations in the population densities of co-located species commonly show asymmetric tail associations; that is, it is common for two species' densities to be more correlated when large than when small, or vice versa. Ordinary measures of association such as correlation do not take this asymmetry into account. Likewise, positively associated fluctuations in the phenology of co-located species also commonly show asymmetric tail associations. We provide evidence that tail associations between two or more species' population-density or phenology time series can be inherited from mutual tail associations of these quantities with an environmental driver. We argue that our understanding of community dynamics and stability, and of phenologies of interacting species, can be meaningfully improved in future work by taking into account tail associations.